When machining spherically-preformed, thin-walled sheet metal parts, as for instance, skin cover sheets of aircraft, it is necessary that the support contact points of such a work piece conform precisely to the shape of the work piece itself while it is being machined, in order to avoid local deformation. To achieve this, a clamping device arranged in a horizontal plane is known from the DE-PS 31 26 720. This known device comprises a head held in a locally fastened base portion together with a negative pressure unit. The clamping element is formed by a receptacle in the form of a semi-spherical shell, which is supported to be movable in a cup-shaped recess of the head. The receptacle is elastically retained at the head by means of a tension spring. Such an embodiment of a clamping device is limited to an arrangement for skin cover sheets to be clamped in a horizontal plane or the like, since the fastening of the clamping element proper with the head is achieved only by means of a tension spring.